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Life span and a new critical exponent for a quasilinear degenerate parabolic equation with slow decay initial values. (English) Zbl 1182.35028
Summary: We consider the positive solution of a Cauchy problem for the following $$p$$-Laplace parabolic equation
$u_t = \text{div}(|\nabla u|^{p-2}\nabla u)+u^q,\quad p>2,\;q>1,$ and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence of global and non-global solutions of the Cauchy problem. Furthermore, the life span of solutions is also studied.

MSC:
 35B33 Critical exponents in context of PDEs 35K65 Degenerate parabolic equations 35B44 Blow-up in context of PDEs 35K92 Quasilinear parabolic equations with $$p$$-Laplacian 35K15 Initial value problems for second-order parabolic equations
Keywords:
slowly decay initial data
Full Text:
References:
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